When using the Add to Salesforce feature, you can choose to save attachments to Salesforce along with the content of the email. By default, those attached files will be saved to the Task record only.
However, if you'd prefer those files to be even more accessible in Salesforce, you can allow them to be saved to the Chatter feed on other related objects like Contacts or Opportunities. By saving to the Chatter, this will also bring the files into either the Notes & Attachments or Files related list.
With Automatic Logging enabled, any outbound emails you send to existing Salesforce leads/contacts will be automatically added to Salesforce (without you having to select the Add to Salesforce button).